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Homothetic packings of centrally symmetric convex bodies
A centrally symmetric convex body is a convex compact set with non-empty interior that is symmetric about the origin. Of particular interest are...
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Mean radii of symmetrizations of a convex body
We study the relation between some successive and mean radii of a convex body and its Steiner, Schwarz, and Minkowski symmetral. In particular, we...
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On the convex hull and homothetic convex hull functions of a convex body
The aim of this note is to investigate the properties of the convex hull and the homothetic convex hull functions of a convex body K in Euclidean n -sp...
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Lipschitz Selectors May Not Yield Competitive Algorithms for Convex Body Chasing
The current best algorithms for the convex body chasing (CBC) problem in online algorithms use the notion of the Steiner point of a convex set. In...
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Affine convex geometry – Part 2
The main objective of this chapter is to study some important (starlike or convex) bodies associated to a given convex body. These are the so-called...
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On star-convex bodies with rotationally invariant sections
We will prove that an origin-symmetric star-convex body K with sufficiently smooth boundary and such that every hyperplane section of K passing...
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Convex sets
Convexity is a very intuitive and geometric notion, but plays a fundamental role in many (also abstract) branches of mathematics. In vector spaces,...
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Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities
In this note we study the systoles of convex hypersurfaces in R2n invariant under an anti-symplectic involution. We investigate a uniform upper bound...
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A Chapter About Asymptotic Geometric Analysis: Isomorphic Position of Centrally Symmetric Convex Bodies
In a few short paragraphs we introduce a relatively new subject named Asymptotic Geometric Analysis (AGA). We discuss two results/discoveries, one...
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From valuations on convex bodies to convex functions
A geometric framework relating valuations on convex bodies to valuations on convex functions is introduced. It is shown that a classical result by...
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Affine convex geometry – Part 1
This chapter is dedicated to the affine geometry of convex bodies (in view of their affine positions). Roughly speaking, we want to discuss how...
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Convex Optimization
Convex optimization or convex programming refers to the problem of minimizing convex functions over convex sets. Observe that we have been careful to...
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Morse–Smale complexes on convex polyhedra
Motivated by applications in geomorphology, the aim of this paper is to extend Morse–Smale theory from smooth functions to the radial distance...
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